In a nutshell;
The celeron chip (Made by Intel) is a PIII chip that only uses half of the on-chip Cache (usually 128kb). This isn't quite technically accurate, but it is a good enough explanation to let you know what you are looking at.
The Duron is AMD's version of a celeron. For the AMD line, either a Thunderbird or Athlon chip (same chip different name) are the equivelent of PIII. The Athlon XP chip is the equiv. of the P4. In most tests the AMD outperforms the Intel chips. If you are upgrading or buying a new pc, that is a worhtwhile consideration.